Imagine a pink Goblin. Give him two very white ears. Now change his color to blue. Make him a bit shorter than he was.
Good. Now where does this Goblin "exist"? In my understanding I have come to accept that "exist" is a loaded word and can suffer from ambiguity of meaning based on different contexts. To say that something exists, like numbers, when considering the pressure inside a tank, is very real and solid discussion material. This goblin, is similar to those numbers but unlike the numbers, this goblin doesn't share a context with a real public physical world we all share. Hence, if you mean by existence, the very fact that it can become knowable, then it does exist. However, that doesn't necessarily imply that what you conjure up in your mind has a physical counterpart.
This may lead some people to incline themselves towards substance dualism, as the goblin you conjured up in your minds eye, has a real experiential effect on your mind. And your mind is apparently causally linked to the physical world, but we don't know which way that link works (the free will debate). You may change your physical actions to include your imaginary goblin, like share a conversation with him, but people might take you for a nutjob if you do it in public.
The point is, mental events that you are able to experience as a objects in consciousness have an existence, but to make that case, one must refine the definition of "existence".